Relational Order, Decision Stability, and Emergent Temporal Structure: A Conjecture Compendium for the Ayala Omega Framework

This compendium develops a unified conjectural extension of the Ayala Ω framework for stochastic decision systems. The starting point is the four-channel task-relative architecture A_J=(Ω_P, Ω_O, Ω_D; D^J), keeping physical feasibility, observability, decision margin, and transformation order distinct. The stability and robustness branch is organized by a common mechanism in which admissible transformations generate task-visible margin responses that are compared with available decision margins. Discrete competing orders yield order-defect quantities, while continuous admissible paths yield orbit-boundary contact laws. Under normalized finite-order contact, nondegenerate leading coefficients, local reachability, and uniform crossing-scale remainder control, the local boundary scale has an inverse-power asymptotic. The framework distinguishes exponent information from amplitude information, finite from flat contact, scalar certificate margins from competitor-resolved exact robustness, and single-branch control from scale-dependent switching. The broader relational-spectrum, irreversibility, predictive-sufficiency, temporal, and relativity branches remain conjectural.